Minimal Sums and Minimal Products (Comp Eng)

[AntiVirus]

Is it true that Minimal Sums are the same as the prime implicates which are the elements that make up the disjunctive normal form? And the minimal products are the same as the prime implicants which are the elements that make up the conjunctive normal formula?

[Chavo]

huh?  I'm considerably farther than you in the CompEn program and I have no idea what you are talking about.

[Sidoh]

huh?  I'm considerably farther than you in the CompEn program and I have no idea what you are talking about.

Different universities have different programs, obviously.  They may have chosen to give him a course in discrete mathematics right off of the bat (maybe you've had it too and it used different language for the terms he's talking about?) or something like that.

I'm not sure what he's talking about either!

[Chavo]

Maybe, I have to take discrete to graduate, but since its not a prereq for any of my classes, I haven't yet.

[Sidoh]

Maybe, I have to take discrete to graduate, but since its not a prereq for any of my classes, I haven't yet.

The CS department here has attempted to integrate discrete math with an introductory programming course, so both subjects progress more slowly than they otherwise would.  We haven't covered the things AV has mentioned, but I assume we will or it will be taught at some point in the CS cirriculum.

[AntiVirus]

My class is Computer Engineering 111.  If that helps?  And I think we learn some of this in CS courses, but later on.  Infact, there are 3 prereq classes that are CS classes to get into this Comp Eng class that I haven't taken yet.  Why am I in this class?  I have no idea! There are only 2 freshmen in this class and I am one of them.

Anyway, I emailed my prof. and he said this:

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Dear Brandon,
 
If you replace "prime" with "essential prime" in your message below, then you will be very close.  The reason why I add the word essential is that you can get a prime implicant or implicate that you wind up not needing, beacuse the function has already been completely specified by other prime implicants.
 
Here's an example that might help you.
Consider the function:
F(A,B,C,D) = sum minterms(3, 4, 5, 7, 9, 13, 14, 15).
 
Note that, when you work it out, BD is a prime implicant.  However, we won't use it in the minimal SOP expression, even though all the other terms have a bunch of 3-input AND gates!  The reason for this is that we are forced to use those terms, for reasons that will become clear when you work through the example.  Although we CAN use the term BD, we don't need it anymore, because we have covered all those 1's by that point anyway.
 
There's one more caveat -- the solution is often not unique.  So, when we have used up all the essential prime implicants, we often have to choose between a couple of equally good ways to mop up the rest of the K-map.  As you work through the rest of the examples, you should see this occurring naturally.
 
Hope this helps.

[AntiVirus]

I sent my prof. back after I worked it.  So here is what I got:

Alright, I worked out the problem and I got this:

Essential Implicants: (not A)CD, (not A)B(not C), A(not C)D, ABC
Minimal Sums: F(A,B,C,D) = ((not A)CD) + ((not A)B(not C)) + (A(not C)D)+ (ABC)

Essential Implicates: (not A)CD, A(not C)D, (not A)B(not C), ABC
Minimal Products: F(A,B,C,D) = ((not A)+C+D)((not A)+B+(not C))(A+(not C)+D)(A+B+C)

Is that right?

As I said in the email, I am not sure if that's correct.  But that's what I got.  Maybe that helps explain what I am talking about?

[Chavo]

ooooooooh

you guys are doing formal logic theory, thats a required CS class here (but optional for CompEn)

Have fun with that, I absolutely abhored the class (it was just proof after proof where you are allowed to assume jack shit)

[AntiVirus]

I don't really like this class.  I think that if I would have taken it later on I would have enjoyed it more, but right now I don't!
*sigh*